Question

$4^{th}$ term in the expansion of $(3-5x{)}^n$ where $x=\frac{1}{5}$, is numerically greatest if $n=$

• A. $7$
• B. $9$
• C. $11$
• D. $16$

Answer 1

Answer: (C)

$11$

$r\le \frac{(n+1)\left(|5x|\right)}{3+|5x|}$
$\Rightarrow r\le \frac{n+1}{4}$
Now it is given that $x=\frac{1}{5}$ and the $4^{th}$ term is numerically the greatest term.
Therefore
$3\le \frac{n+1}{4}\le 4$
$12\le (n+1)\le 16$
$11\le \left(n\right)\le 15$
Hence $n=(11,12,13,14,15)$